Errors are part of the process of problem solving, which implies that both teachers and learners need to be more tolerant of them, Mr. Martinez points out. If no mistakes are made, then almost certainly no problem solving is taking place. To think is constantly to choose in view of the end to be pursued.(1) Every educator is familiar with the term "problem solving," and most would agree that the ability to solve problems is a worthy goal of education. But what is problem solving? Its meaning is actually quite straightforward: problem solving is the process of moving toward a goal when the path to that goal is uncertain. We solve problems every time we achieve something without having known beforehand how to do so. We encounter simple problems every day: finding lost keys, deciding what to do when our car won't start, even improvising a meal from leftovers. But there are also larger and more significant "ill-defined" problems, such as getting an education, becoming a successful person, and finding happiness. Indeed, the most important kinds of human activities involve accomplishing goals without a script. Problem solving is a ubiquitous feature of human functioning. Human beings are problem solvers who think and act within a grand complex of fuzzy and shifting goals and changing means to attain them. This has always been true, but it is doubly so today because we live in a time of unprecedented societal transformation. When circumstances change, old procedures no longer work. To adapt is to pursue valued goals even when circumstances - and perhaps the goals themselves - are in flux. Because the pace of societal change shows no signs of slackening, citizens of the 21st century must become adept problem solvers, able to wrestle with ill-defined problems and win. Problem-solving ability is the cognitive passport to the future. There is no formula for true problem solving. If we know exactly how to get from point A to point B, then reaching point B does not involve problem solving. Think of problem solving as working your way through a maze.(2) In negotiating a maze, you make your way toward your goal step by step, making some false moves but gradually moving closer toward the intended end point. What guides your choices? Perhaps a rule like this: choose the path that seems to result in some progress toward the goal. Such a rule is one example of a heuristic. A heuristic is a rule of thumb. It is a strategy that is powerful and general, but not absolutely guaranteed to work. Heuristics are crucial because they are the tools by which problems are solved. By contrast, algorithms are straightforward procedures that are guaranteed to work every time. For example, you have in your long-term memory algorithms that enable you to tie your shoelaces, to start up your car, and perhaps even to cook an omelet. Barring broken shoelaces, a dead battery, and rotten eggs, these algorithms serve you very well. An algorithm may even be so automatic that it requires very little conscious processing as you carry out the procedure. Now here is an important consideration: what constitutes problem solving varies from person to person. For a small child, tying shoelaces will indeed require problem solving, just as cooking an omelet entails problem solving for many adults. Thus problem solving involves an interaction of a person's experience and the demands of the task. Once we have mastered a skill, we are no longer engaged in problem solving when we apply it. For a task to require problem solving again, novel elements or new circumstances must be introduced or the level of challenge must be raised. Some problem solutions, however, can never be reduced to algorithms, and it is often those problems that constitute the most profound and rewarding of human activities. The necessity of problem solving to all that is important about being a person cannot be overstated. In addition, problem solving is not an advanced process that is reserved solely for mature learners. …